﻿Some 
  Relations 
  in 
  Capillarity. 
  491 
  

  

  Table 
  III. 
  

  

  I 
  ^° 
  

  

  •on 
  

  

  •0053 
  

  

  •0042 
  

  

  •0042 
  •OOSO 
  

  

  •0055 
  

  

  The 
  quantities 
  in 
  Table 
  II. 
  seem 
  to 
  exhibit 
  no 
  regular 
  

   increase 
  or 
  decrease 
  from 
  one 
  column 
  to 
  another^ 
  but 
  this 
  is 
  

   due 
  to 
  the 
  conflict 
  between 
  the 
  decay 
  due 
  to 
  the 
  internal 
  

   friction 
  and 
  the 
  decay 
  due 
  to 
  the 
  bottom 
  of 
  the 
  trough. 
  

  

  Clare 
  College, 
  

   Cambridore. 
  

  

  LYI. 
  Some 
  Relations 
  in 
  Capillarity. 
  By 
  R. 
  D. 
  Kleeman, 
  

   D.SCf 
  B.A., 
  Research 
  Student 
  of 
  Emmanuel 
  College, 
  

   Cambridge, 
  and 
  McKinnon 
  Student 
  of 
  tlie 
  Royal 
  Society*. 
  

  

  THE 
  potential 
  energy 
  of 
  the 
  surface 
  of 
  a 
  liquid 
  due 
  to 
  the 
  

   attractions 
  between 
  its 
  molecules 
  has 
  been 
  calculated 
  

   in 
  general 
  terms 
  by 
  Einstein. 
  Einstein'^s 
  line 
  of 
  reasoning 
  

   is 
  as 
  follows. 
  The 
  potential 
  energy 
  of 
  a 
  mass 
  of 
  liquid 
  is 
  

   first 
  considered. 
  It 
  is 
  assumed 
  that 
  the 
  potential 
  energy 
  of 
  

   two 
  molecules 
  is 
  given 
  by 
  the 
  expression'?^— 
  c*iC2'v|^(r) 
  where 
  

   '«/r(r) 
  is 
  some 
  function 
  of 
  the 
  distance 
  between 
  the 
  molecules 
  

   and 
  Ci 
  and 
  C2 
  are 
  constants 
  depending 
  upon 
  the 
  molecules. 
  

   For 
  n 
  molecules 
  the 
  second 
  term 
  is 
  replaced 
  by 
  

  

  it 
  ^ 
  c^c^fir^,^). 
  

  

  If 
  the 
  molecules 
  are 
  identical 
  this 
  becomes 
  

  

  a=7i 
  (3 
  = 
  71 
  

   a=l 
  (5 
  = 
  1 
  

  

  It 
  is 
  next 
  assumed 
  that 
  the 
  potential 
  is 
  the 
  same 
  as 
  if 
  the 
  

   matter 
  were 
  distributed 
  evenly 
  in 
  space. 
  The 
  potential 
  

   energy 
  may 
  now 
  be 
  written 
  

  

  where 
  dr 
  and 
  dr^ 
  are 
  elements 
  of 
  volume 
  occupied 
  by 
  matter 
  

   and 
  X 
  is 
  the 
  number 
  of 
  molecules 
  in 
  unit 
  volume. 
  If 
  each 
  

   molecule 
  consists 
  of 
  several 
  atoms, 
  we 
  may 
  put 
  c 
  = 
  tca 
  as 
  is 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  